Evolution of superoscillatory initial data in several variables in uniform electric field

Y. Aharonov, F. Colombo, I. Sabadini, D. C. Struppa, J. Tollaksen

Research output: Contribution to journalArticlepeer-review

Abstract

A superoscillating function is defined by the property that it oscillates faster than its fastest Fourier components. This is mathematically possible because the coefficients of the linear combinations of the band limited components depend on the number of components. This phenomenon was discovered in the context of quantum physics, but it has important applications in a variety of areas, including metrology, antenna theory, and a new theory of superresolution in optics. In this paper we study the evolution of superoscillatory functions in uniform electric field by the Schrödinger equation where we assume that the Hamiltonian contains a even polynomial of the linear momentum p. This includes the classical case but also relativistic corrections of any order. Moreover, we extend our results to the case of several variables using the theory of superoscillating functions in several variables. We conclude by discussing a comparison of our work with the existing literature.

Original languageEnglish
Article number185201
JournalJournal of Physics A: Mathematical and Theoretical
Volume50
Issue number18
DOIs
StatePublished - 30 Mar 2017
Externally publishedYes

Keywords

  • Fourier transform
  • Schrodinger equation in uniform electric field
  • superoscillating functions in several variables

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